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A theoretical study of the write, read, and erase processes in electrical scanning probe storage on phase-change media is presented. Electrical, thermal, and phase-transformation mechanisms are considered to produce a physically realistic description of this new approach to ultrahigh-density data storage. Models developed are applied to the design of a suitable storage layer stack with the necessary electrical, thermal, and tribological properties to support recorded bits of nanometric scale. The detailed structure of nanoscale crystalline and amorphous bits is also predicted. For an optimized trilayer stack comprising Ge2Sb2Te5 sandwiched by amorphous or diamond-like carbon layers, crystalline bits were roughly trapezoidal in shape while amorphous bits were semi-ellipsoidal. In both cases, the energy required to write individual bits was very low (of the order of a few hundred picoJoules). Amorphous marks could be directly overwritten (erased), but crystalline bits could not. Readout performance was investigated by calculating the readout current as the tip scanned over isolated bits and bit patterns of increasing density. The highest readout contrast was generated by isolated crystalline bits in an amorphous matrix, but the narrowest readout pulses arose from isolated amorphous marks in a crystalline background. To assess the ultimate density capability of electrical probe recording the role of write-induced intersymbol interference and the thermodynamic stability of nanoscale marks were also studied.